There are three different ways that two lines can interact.
I. Intersecting Lines

Intersecting lines are lines that
meet.
There are two important
factors with two intersecting lines:
A) Two lines will
intersect in a single point. This point is a point of each line.
B) There's no way to
construct two straight lines and have them intersect in more than one
point.
II. Parallel Lines
Parallel lines are lines that never meet. A set of parallel lines
always travels in the same direction.

Parallel lines always stay equal distance from
each
other.
II. Skew Lines
Skew lines do not intersect, but they do
not travel in the same direction.
Skew lines cannot exist in two dimensions.
The figure below is turning on the 'y axis' to give you a better look
at two skew lines.
The skew lines are the blue
and green lines. The black
lines are the axes.
Notice how they do not intersect but are not parallel.

For a stereographic (or
3D) representation of skew lines, click here.
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